I am self-studying the deep learning book by Goodfellow, Bengio and Courville(https://www.deeplearningbook.org/contents/ml.html). On page 100, it has a brief introduction to classification with missing inputs as the following:

"When some of the inputs may be missing, rather than providing a single classification function, the learning algorithm must learn a set of functions... One way to efficiently define such a large set of functions is to learn a probability distribution over all of the relevant variables, then solve the classification task by marginalizing out the missing variables. With n input variables, we can now obtain all $2^n$ different classification functions needed for each possible set of missing inputs, but we only need to learn a single function describing the joint probability distribution. See Goodfellow et al. (2013b) for an example of a deep probabilistic model applied to such a task in this way. "

Does anyone know what exactly the joint probability distribution function that we want to learn is and how we use it to obtain information from the single function (described as "marginalizing out the missing variables")?


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